\[ \begin{array}{l}\text { Solve the following inequality and give the solution in interval notation. } \\ \text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { A. The solution set in the interval notation is } \\ \text { (Use integers or fractions for any numbers in the expression.) } \\ \text { B. The solution set is the empty set. }\end{array} \]
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To solve an inequality, it's essential first to isolate the variable on one side. For example, if you have \( x + 3 < 7 \), you'd subtract 3 from both sides to get \( x < 4 \). This means any number less than 4 is a solution. In interval notation, this is expressed as \( (-\infty, 4) \). Always check the endpoints as well, ensuring you're capturing the correct solutions. When working with inequalities, a common mistake is flipping the inequality sign when multiplying or dividing by a negative number. For instance, if you have \( -2x > 4 \) and you divide by -2, you need to flip the inequality to \( x < -2 \). Failing to do so can lead to incorrect solutions, so be cautious!